Geodesic
A Kronecker-Type Theorem for Complex Polynomials in Several Variables
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 447-452

Voir la notice de l'article provenant de la source Cambridge University Press

We give a classification result for "extreme-monic" polynomials in several variables having measure 1. The result implies a recent several-variable generalization, by D. W. Boyd, of Kronecker's classical theorem (that all zeros of a monic integral polynomial, with non-zero constant term and measure 1, are roots of unity). 
Smyth, C. J. A Kronecker-Type Theorem for Complex Polynomials in Several Variables. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 447-452. doi: 10.4153/CMB-1981-068-8
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[1] 1. Boyd, D. W., Kronecker's theorem and Lehmefs problem for polynomials in several variables, (to appear). Google Scholar

[2] 2. Clarke, B. L., Asymptotes and intercepts of real-power polynomial surfaces from the geometry of the exponent polytope, SIAM J. Appl. Math. 35 (1978), 755-786. Google Scholar

[3] 3. Kelly, P. J. and Weiss, M. L., Geometry and Convexity (John Wiley and Sons, New York 1979). Google Scholar

[4] 4. Kronecker, L., Zwei Sàtze ùber Gleichungen mit ganzzahligen Coefficienten, J. reine angew. Math. 53 (1857), 173-175. Google Scholar

[5] 5. Lawton, W., Asymptotic properties of roots of polynomials -preliminary report, Proceedings 7th National Mathematics Conference, Dept. Math. Azarabadegan Univ., Tabriz, 1976. Google Scholar

[6] 6. Montgomery, H. L. and Schinzel, A., Some arithmetic properties of polynomials in several variables, in Transcendence Theory: Advances and Applications, Baker, A. and Masser, D. W. (editors) (Academic Près 1977). Google Scholar

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